Question

The expected values, variances and standard Deviatiations for two random variables X and Y are given in the following table

Variable	expected value	variance	standard deviation
X	20	9	3
Y	35	25	5

Find the expected value and standard deviation of the following combinations of the variable X and Y. Round to nearest whole number.

E(X+10) =  ,

StDev(X+10) =

E(2X) =  ,

StDev(2X) =

E(3X-2) =  ,

StDev(3X-2) =

E(3X +4Y) =  ,

StDev(3X+4Y) =

E(X-2Y) =  ,

StDev(X-2Y) =

Answer 1

E(X + 10) = E(X) + 10 = 20 + 10 = 30

SD(X + 10) = SD(X) + SD(10) = 3 + 0 = 3

E(2X) = 2 * E(X) = 2 * 20 = 40

SD(2X) = 2 * SD(X) = 2 * 3 = 6

E(3X - 2) = 3 * E(X) - 2 = 3 * 20 - 2 = 58

SD(3X - 2) = 3 * SD(X) - 0 = 3 * 3 = 9

E(3X + 4Y) = 3 * E(X) + 4 * E(Y) = 3 * 20 + 4 * 35 = 200

SD(3X + 4Y) = sqrt(Var(3X + 4Y)) = sqrt(3² * Var(X) + 4² * Var(Y)) = sqrt(9 * 9 + 16 * 25) = 22

E(X - 2Y) = E(X) - 2 * E(Y) = 20 - 2 * 35 = -50

SD(X - 2Y) = sqrt(Var(X - 2Y)) = sqrt(Var(X) + (-2)² * Var(Y)) = sqrt(9 + 4 * 25) = 10